Fachgebiet Wissensverarbeitung (KDE), EECS, Universität Kassel

Das Fachgebiet Wissensverarbeitung des Fachbereichs Elektrotechnik/Informatik forscht an der Entwicklung von Methoden zur Wissensentdeckung und Wissensrepräsentation (Approximation und Exploration von Wissen, Ordnungsstrukturen in Wissen, Ontologieentwicklung) in Daten als auch in der Analyse von (sozialen) Netzwerkdaten und damit verbundenen Wissensprozessen (Metriken in Netzwerken, Anomalieerkennung, Charakterisierung von sozialen Netzwerken). Dabei liegt ein Schwerpunkt auf der exakten algebraischen Modellierung der verwendeten Strukturen und auf der Evaluierung und Neuentwicklung von Netzwerkmaßen. Neben der Erforschung von Grundlagen in den Gebieten Ordnungs- und Verbandstheorie, Beschreibungslogiken, Graphentheorie und Ontologie werden auch Anwendungen – bspw. in sozialen Medien sowie in der Szientometrie – erforscht.

Das Fachgebiet Wissensverarbeitung ist Mitglied im Wissenschaftlichen Zentrum für Informationstechnik-Gestaltung (ITeG) und im Wissenschaftlichen Zentrum INCHER der Universität Kassel, sowie im Hessischen KI-Zentrum (hessian.AI).

Unsere neusten Publikationen

• 1.

  Sharma, A., Nöhre, M., Stumme, G.: Exploring ESC Winners with Nested Diagrams, https://arxiv.org/abs/2608.13630, (2026). https://doi.org/https://doi.org/10.48550/arXiv.2608.13630.

  URLBibTeXEndNoteDOI

  We present ConceptFlow, a scikit-learn-compatible Python library for Formal Concept Analysis that constructs and renders nested line diagrams from many-valued formal contexts. Given a many-valued context and a partition of its attributes into conceptual scales, ConceptFlow performs conceptual scaling, computes the factor lattices, identifies filled nodes of the corresponding subdirect product, and produces an interactive visualization. We apply ConceptFlow to the winners of the Eurovision Song Contest from 1975 to 2025, exploring relationships between voting patterns and musical characteristics. Voting support is captured by an outer scale spanning regional, cultural, historical, and political dimensions, while an inner scale captures musical characteristics via tempo and key. The resulting nested line diagram reveals implications across both scales, exposing dependencies between how winning entries were voted for and the musical properties they share.

  @misc{sharma2026exploringescwinnersnested,
  abstract = {We present ConceptFlow, a scikit-learn-compatible Python library for Formal Concept Analysis that constructs and renders nested line diagrams from many-valued formal contexts. Given a many-valued context and a partition of its attributes into conceptual scales, ConceptFlow performs conceptual scaling, computes the factor lattices, identifies filled nodes of the corresponding subdirect product, and produces an interactive visualization. We apply ConceptFlow to the winners of the Eurovision Song Contest from 1975 to 2025, exploring relationships between voting patterns and musical characteristics. Voting support is captured by an outer scale spanning regional, cultural, historical, and political dimensions, while an inner scale captures musical characteristics via tempo and key. The resulting nested line diagram reveals implications across both scales, exposing dependencies between how winning entries were voted for and the musical properties they share.},
  author = {Sharma, Anurag and Nöhre, Marcel and Stumme, Gerd},
  keywords = {itegpub},
  month = {08},
  title = {Exploring ESC Winners with Nested Diagrams},
  year = 2026
  }
  

  %0 Generic
  %1 sharma2026exploringescwinnersnested
  %A Sharma, Anurag
  %A Nöhre, Marcel
  %A Stumme, Gerd
  %D 2026
  %R https://doi.org/10.48550/arXiv.2608.13630
  %T Exploring ESC Winners with Nested Diagrams
  %U https://arxiv.org/abs/2608.13630
  %X We present ConceptFlow, a scikit-learn-compatible Python library for Formal Concept Analysis that constructs and renders nested line diagrams from many-valued formal contexts. Given a many-valued context and a partition of its attributes into conceptual scales, ConceptFlow performs conceptual scaling, computes the factor lattices, identifies filled nodes of the corresponding subdirect product, and produces an interactive visualization. We apply ConceptFlow to the winners of the Eurovision Song Contest from 1975 to 2025, exploring relationships between voting patterns and musical characteristics. Voting support is captured by an outer scale spanning regional, cultural, historical, and political dimensions, while an inner scale captures musical characteristics via tempo and key. The resulting nested line diagram reveals implications across both scales, exposing dependencies between how winning entries were voted for and the musical properties they share.
  

• 1.

  Nöhre, M., Dürrschnabel, D., Ganter, B., Stumme, G.: A Visual Benchmark of DimFlux: Comparison of Line Diagrams for Concept Lattices, https://doi.org/10.5281/zenodo.20280441, (2026). https://doi.org/10.5281/zenodo.20280441.

  URLBibTeXEndNoteDOI

  @misc{nohre_2026_20280441,
  author = {Nöhre, Marcel and Dürrschnabel, Dominik and Ganter, Bernhard and Stumme, Gerd},
  keywords = {itegpub},
  month = {05},
  publisher = {Zenodo},
  title = {A Visual Benchmark of DimFlux: Comparison of Line Diagrams for Concept Lattices},
  year = 2026
  }
  

  %0 Generic
  %1 nohre_2026_20280441
  %A Nöhre, Marcel
  %A Dürrschnabel, Dominik
  %A Ganter, Bernhard
  %A Stumme, Gerd
  %D 2026
  %I Zenodo
  %R 10.5281/zenodo.20280441
  %T A Visual Benchmark of DimFlux: Comparison of Line Diagrams for Concept Lattices
  %U https://doi.org/10.5281/zenodo.20280441
  

• 1.

  Tolzin, A., Hille, T., Knoth, N., Janson, A.: Mining Hidden Prompt Engineering Patterns with Formal Concept Analysis and Association Rules. In: Bui, T.X. (ed.) 59th Hawaii International Conference on System Sciences, {HICSS} 2026. ScholarSpace (2026).

  URLBibTeXEndNote

  @inproceedings{Tolzin2026Jan,
  author = {Tolzin, Antonia and Hille, Tobias and Knoth, Nils and Janson, Andreas},
  booktitle = {59th Hawaii International Conference on System Sciences, {HICSS} 2026},
  editor = {Bui, Tung X.},
  keywords = {itegpub},
  month = {01},
  publisher = {ScholarSpace},
  title = {Mining Hidden Prompt Engineering Patterns with Formal Concept Analysis and Association Rules},
  year = 2026
  }
  

  %0 Conference Paper
  %1 Tolzin2026Jan
  %A Tolzin, Antonia
  %A Hille, Tobias
  %A Knoth, Nils
  %A Janson, Andreas
  %B 59th Hawaii International Conference on System Sciences, {HICSS} 2026
  %D 2026
  %E Bui, Tung X.
  %I ScholarSpace
  %T Mining Hidden Prompt Engineering Patterns with Formal Concept Analysis and Association Rules
  %U https://hdl.handle.net/10125/111529
  %@ 978-0-9981331-9-5
  

• 1.

  Nöhre, M., Dürrschnabel, D., Ganter, B., Stumme, G.: DimFlux: Force-directed additive line diagrams. International Journal of Approximate Reasoning. 197, 109734 (2026). https://doi.org/https://doi.org/10.1016/j.ijar.2026.109734.

  URLBibTeXEndNoteDOI

  The visualization of concept lattices is a central problem in the field of Formal Concept Analysis. Force-directed algorithms, as popular in graph drawing, are a promising approach, treating lattice diagrams as physical models, optimizing node positions based on forces derived from the lattice structure. We build on the work of Zschalig, who, however, limited himself to attribute-additive diagrams. We use a more general additivity, in which both the attributes and the objects contribute to the positions of the concept nodes. We replace the planarity enhancer used by Zschalig to obtain a starting diagram for force-directed optimization with the DimDraw algorithm, which generates structured order diagrams on its own. The combination results in DimFlux, an algorithm that leverages the advantages of DimDraw but generates additive diagrams in which readability is increased by maximizing the conflict distance between nodes and non-incident edges.

  @article{NOHRE2026109734,
  abstract = {The visualization of concept lattices is a central problem in the field of Formal Concept Analysis. Force-directed algorithms, as popular in graph drawing, are a promising approach, treating lattice diagrams as physical models, optimizing node positions based on forces derived from the lattice structure. We build on the work of Zschalig, who, however, limited himself to attribute-additive diagrams. We use a more general additivity, in which both the attributes and the objects contribute to the positions of the concept nodes. We replace the planarity enhancer used by Zschalig to obtain a starting diagram for force-directed optimization with the DimDraw algorithm, which generates structured order diagrams on its own. The combination results in DimFlux, an algorithm that leverages the advantages of DimDraw but generates additive diagrams in which readability is increased by maximizing the conflict distance between nodes and non-incident edges.},
  author = {Nöhre, Marcel and Dürrschnabel, Dominik and Ganter, Bernhard and Stumme, Gerd},
  journal = {International Journal of Approximate Reasoning},
  keywords = {itegpub},
  pages = 109734,
  title = {DimFlux: Force-directed additive line diagrams},
  volume = 197,
  year = 2026
  }
  

  %0 Journal Article
  %1 NOHRE2026109734
  %A Nöhre, Marcel
  %A Dürrschnabel, Dominik
  %A Ganter, Bernhard
  %A Stumme, Gerd
  %D 2026
  %J International Journal of Approximate Reasoning
  %P 109734
  %R https://doi.org/10.1016/j.ijar.2026.109734
  %T DimFlux: Force-directed additive line diagrams
  %U https://www.sciencedirect.com/science/article/pii/S0888613X2600109X
  %V 197
  %X The visualization of concept lattices is a central problem in the field of Formal Concept Analysis. Force-directed algorithms, as popular in graph drawing, are a promising approach, treating lattice diagrams as physical models, optimizing node positions based on forces derived from the lattice structure. We build on the work of Zschalig, who, however, limited himself to attribute-additive diagrams. We use a more general additivity, in which both the attributes and the objects contribute to the positions of the concept nodes. We replace the planarity enhancer used by Zschalig to obtain a starting diagram for force-directed optimization with the DimDraw algorithm, which generates structured order diagrams on its own. The combination results in DimFlux, an algorithm that leverages the advantages of DimDraw but generates additive diagrams in which readability is increased by maximizing the conflict distance between nodes and non-incident edges.
  

• 1.

  Nöhre, M., Stumme, G.: Node Labeling in Line Diagrams of Ordered Sets, https://arxiv.org/abs/2607.23283, (2026). https://doi.org/https://doi.org/10.48550/arXiv.2607.23283.

  URLBibTeXEndNoteDOI

  We propose a flexible, two-phase algorithm for labeling line diagrams of ordered sets, in which the nodes of direct neighbors in the order relation are connected by a straight, upward-pointing line. In contrast to the labeling of diagrams of arbitrary graphs, we benefit from the fact that all edges in line diagrams of ordered sets are more or less vertical. In this paper, we study the placement of all labels such that they do not intersect with any nodes, lines, or other labels while minimizing the distances between the nodes and their labels. Our approach starts by filtering the fixed-position model using line diagram-specific readability criteria. For labels that cannot be placed adjacent to their node (overflow labels), we exploit the free space in the graph's interior or the infinite space surrounding the drawing and link the labels with their respective node by straight binding lines that should not cross other nodes or labels if possible. To balance quality and runtime, we derive an initial placement of the overflow labels using a cost function over a sparse grid of candidates, followed by a force-based refinement step to fine-tune the layout. Furthermore, we demonstrate the flexibility of this approach by applying it to the visual constraints of line diagrams in the field of Formal Concept Analysis (FCA), where certain labels have to be placed above their node and others below. This special version of the algorithm shows that a pre-filtering in the first phase and minimal adjustments for the cost function and force-based model are sufficient to handle the dual labeling requirements of concept lattices.

  @misc{nöhre2026nodelabelinglinediagrams,
  abstract = {We propose a flexible, two-phase algorithm for labeling line diagrams of ordered sets, in which the nodes of direct neighbors in the order relation are connected by a straight, upward-pointing line. In contrast to the labeling of diagrams of arbitrary graphs, we benefit from the fact that all edges in line diagrams of ordered sets are more or less vertical. In this paper, we study the placement of all labels such that they do not intersect with any nodes, lines, or other labels while minimizing the distances between the nodes and their labels. Our approach starts by filtering the fixed-position model using line diagram-specific readability criteria. For labels that cannot be placed adjacent to their node (overflow labels), we exploit the free space in the graph's interior or the infinite space surrounding the drawing and link the labels with their respective node by straight binding lines that should not cross other nodes or labels if possible. To balance quality and runtime, we derive an initial placement of the overflow labels using a cost function over a sparse grid of candidates, followed by a force-based refinement step to fine-tune the layout. Furthermore, we demonstrate the flexibility of this approach by applying it to the visual constraints of line diagrams in the field of Formal Concept Analysis (FCA), where certain labels have to be placed above their node and others below. This special version of the algorithm shows that a pre-filtering in the first phase and minimal adjustments for the cost function and force-based model are sufficient to handle the dual labeling requirements of concept lattices.},
  author = {Nöhre, Marcel and Stumme, Gerd},
  howpublished = {arXiv},
  keywords = {itegpub},
  month = {07},
  title = {Node Labeling in Line Diagrams of Ordered Sets},
  year = 2026
  }
  

  %0 Generic
  %1 nöhre2026nodelabelinglinediagrams
  %A Nöhre, Marcel
  %A Stumme, Gerd
  %D 2026
  %R https://doi.org/10.48550/arXiv.2607.23283
  %T Node Labeling in Line Diagrams of Ordered Sets
  %U https://arxiv.org/abs/2607.23283
  %X We propose a flexible, two-phase algorithm for labeling line diagrams of ordered sets, in which the nodes of direct neighbors in the order relation are connected by a straight, upward-pointing line. In contrast to the labeling of diagrams of arbitrary graphs, we benefit from the fact that all edges in line diagrams of ordered sets are more or less vertical. In this paper, we study the placement of all labels such that they do not intersect with any nodes, lines, or other labels while minimizing the distances between the nodes and their labels. Our approach starts by filtering the fixed-position model using line diagram-specific readability criteria. For labels that cannot be placed adjacent to their node (overflow labels), we exploit the free space in the graph's interior or the infinite space surrounding the drawing and link the labels with their respective node by straight binding lines that should not cross other nodes or labels if possible. To balance quality and runtime, we derive an initial placement of the overflow labels using a cost function over a sparse grid of candidates, followed by a force-based refinement step to fine-tune the layout. Furthermore, we demonstrate the flexibility of this approach by applying it to the visual constraints of line diagrams in the field of Formal Concept Analysis (FCA), where certain labels have to be placed above their node and others below. This special version of the algorithm shows that a pre-filtering in the first phase and minimal adjustments for the cost function and force-based model are sufficient to handle the dual labeling requirements of concept lattices.
  

• 1.

  Hirth, J., Hanika, T.: The Geometric Structure of Topic Models. In: Cellier, P., Ganter, B., and Missaoui, R. (eds.) CONCEPTS. pp. 19–34. Springer (2025).

  URLBibTeXEndNote

  @inproceedings{conf/concepts/HirthH25,
  author = {Hirth, Johannes and Hanika, Tom},
  booktitle = {CONCEPTS},
  crossref = {conf/concepts/2025},
  editor = {Cellier, Peggy and Ganter, Bernhard and Missaoui, Rokia},
  keywords = {itegpub},
  pages = {19-34},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {The Geometric Structure of Topic Models.},
  volume = 15941,
  year = 2025
  }
  

  %0 Conference Paper
  %1 conf/concepts/HirthH25
  %A Hirth, Johannes
  %A Hanika, Tom
  %B CONCEPTS
  %D 2025
  %E Cellier, Peggy
  %E Ganter, Bernhard
  %E Missaoui, Rokia
  %I Springer
  %P 19-34
  %T The Geometric Structure of Topic Models.
  %U http://dblp.uni-trier.de/db/conf/concepts/concepts2025.html#HirthH25
  %V 15941
  %@ 978-3-032-03364-2
  

• 1.

  Stubbemann, M., Hille, T., Hanika, T.: Unsupervised Selection of Features by Their Resilience to the Curse of Dimensionality. In: Braun, T., Paaßen, B., and Stolzenburg, F. (eds.) KI. pp. 161–174. Springer (2025).

  URLBibTeXEndNote

  @inproceedings{conf/ki/StubbemannHH25,
  author = {Stubbemann, Maximilian and Hille, Tobias and Hanika, Tom},
  booktitle = {KI},
  crossref = {conf/ki/2025},
  editor = {Braun, Tanya and Paaßen, Benjamin and Stolzenburg, Frieder},
  keywords = {itegpub},
  pages = {161-174},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Unsupervised Selection of Features by Their Resilience to the Curse of Dimensionality.},
  volume = 15956,
  year = 2025
  }
  

  %0 Conference Paper
  %1 conf/ki/StubbemannHH25
  %A Stubbemann, Maximilian
  %A Hille, Tobias
  %A Hanika, Tom
  %B KI
  %D 2025
  %E Braun, Tanya
  %E Paaßen, Benjamin
  %E Stolzenburg, Frieder
  %I Springer
  %P 161-174
  %T Unsupervised Selection of Features by Their Resilience to the Curse of Dimensionality.
  %U http://dblp.uni-trier.de/db/conf/ki/ki2025.html#StubbemannHH25
  %V 15956
  %@ 978-3-032-02813-6
  

• 1.

  de Portugal Mecke, D.C., Alyoussef, H., Stubbemann, M., Koloiarov, I., Hanika, T., Schmidt-Thieme, L.: STADE: Standard Deviation as a Pruning Metric, https://arxiv.org/abs/2503.22451, (2025).

  URLBibTeXEndNote

  @misc{mecke2025stadestandarddeviationpruning,
  author = {de Portugal Mecke, Diego Coello and Alyoussef, Haya and Stubbemann, Maximilian and Koloiarov, Ilia and Hanika, Tom and Schmidt-Thieme, Lars},
  keywords = {itegpub},
  title = {STADE: Standard Deviation as a Pruning Metric},
  year = 2025
  }
  

  %0 Generic
  %1 mecke2025stadestandarddeviationpruning
  %A de Portugal Mecke, Diego Coello
  %A Alyoussef, Haya
  %A Stubbemann, Maximilian
  %A Koloiarov, Ilia
  %A Hanika, Tom
  %A Schmidt-Thieme, Lars
  %D 2025
  %T STADE: Standard Deviation as a Pruning Metric
  %U https://arxiv.org/abs/2503.22451
  

• 1.

  Gutekunst, K.M., D{ü}rrschnabel, D., Hirth, J., Stumme, G.: Conceptual Topic Aggregation. In: Cellier, P., Ganter, B., and Missaoui, R. (eds.) Conceptual Knowledge Structures. pp. 3–18. Springer Nature Switzerland, Cham (2025).

  BibTeXEndNote

  The vast growth of data has rendered traditional manual inspection infeasible, necessitating the adoption of computational methods for efficient data exploration. Topic modeling has emerged as a powerful tool for analyzing large-scale textual datasets, enabling the extraction of latent semantic structures. However, existing methods for topic modeling often struggle to provide interpretable representations that facilitate deeper insights into data structure and content.

  @inproceedings{10.1007/978-3-032-03364-2_1,
  abstract = {The vast growth of data has rendered traditional manual inspection infeasible, necessitating the adoption of computational methods for efficient data exploration. Topic modeling has emerged as a powerful tool for analyzing large-scale textual datasets, enabling the extraction of latent semantic structures. However, existing methods for topic modeling often struggle to provide interpretable representations that facilitate deeper insights into data structure and content.},
  address = {Cham},
  author = {Gutekunst, Klara M. and D{ü}rrschnabel, Dominik and Hirth, Johannes and Stumme, Gerd},
  booktitle = {Conceptual Knowledge Structures},
  editor = {Cellier, Peggy and Ganter, Bernhard and Missaoui, Rokia},
  keywords = {topic_aggregation},
  pages = {3--18},
  publisher = {Springer Nature Switzerland},
  title = {Conceptual Topic Aggregation},
  year = 2025
  }
  

  %0 Conference Paper
  %1 10.1007/978-3-032-03364-2_1
  %A Gutekunst, Klara M.
  %A D{ü}rrschnabel, Dominik
  %A Hirth, Johannes
  %A Stumme, Gerd
  %B Conceptual Knowledge Structures
  %C Cham
  %D 2025
  %E Cellier, Peggy
  %E Ganter, Bernhard
  %E Missaoui, Rokia
  %I Springer Nature Switzerland
  %P 3--18
  %T Conceptual Topic Aggregation
  %X The vast growth of data has rendered traditional manual inspection infeasible, necessitating the adoption of computational methods for efficient data exploration. Topic modeling has emerged as a powerful tool for analyzing large-scale textual datasets, enabling the extraction of latent semantic structures. However, existing methods for topic modeling often struggle to provide interpretable representations that facilitate deeper insights into data structure and content.
  %@ 978-3-032-03364-2
  

• 1.

  Abdulla, M., Hille, T., D{ü}rrschnabel, D., Stumme, G.: Rises for Measuring Local Distributivity in Lattices. In: Cellier, P., Ganter, B., and Missaoui, R. (eds.) Conceptual Knowledge Structures. pp. 392–407. Springer Nature Switzerland, Cham (2025).

  BibTeXEndNote

  Distributivity is a well-established and extensively studied notion in lattice theory. In the context of data analysis, particularly within Formal Concept Analysis (FCA), lattices are often observed to exhibit a high degree of distributivity. However, no standardized measure exists to quantify this property. In this paper, we introduce the notion of rises in (concept) lattices as a means to assess distributivity. Rises capture how the number of attributes or objects in covering concepts change within the concept lattice. We show that a lattice is distributive if and only if no non-unit rises occur. Furthermore, we relate rises to the classical notion of meet- and join distributivity. We observe that concept lattices from real-world data are to a high degree join-distributive, but much less meet-distributive. We additionally study how join-distributivity manifests on the level of ordered sets.

  @inproceedings{10.1007/978-3-032-03364-2_25,
  abstract = {Distributivity is a well-established and extensively studied notion in lattice theory. In the context of data analysis, particularly within Formal Concept Analysis (FCA), lattices are often observed to exhibit a high degree of distributivity. However, no standardized measure exists to quantify this property. In this paper, we introduce the notion of rises in (concept) lattices as a means to assess distributivity. Rises capture how the number of attributes or objects in covering concepts change within the concept lattice. We show that a lattice is distributive if and only if no non-unit rises occur. Furthermore, we relate rises to the classical notion of meet- and join distributivity. We observe that concept lattices from real-world data are to a high degree join-distributive, but much less meet-distributive. We additionally study how join-distributivity manifests on the level of ordered sets.},
  address = {Cham},
  author = {Abdulla, Mohammad and Hille, Tobias and D{ü}rrschnabel, Dominik and Stumme, Gerd},
  booktitle = {Conceptual Knowledge Structures},
  editor = {Cellier, Peggy and Ganter, Bernhard and Missaoui, Rokia},
  keywords = {itegpub},
  pages = {392--407},
  publisher = {Springer Nature Switzerland},
  title = {Rises for Measuring Local Distributivity in Lattices},
  year = 2025
  }
  

  %0 Conference Paper
  %1 10.1007/978-3-032-03364-2_25
  %A Abdulla, Mohammad
  %A Hille, Tobias
  %A D{ü}rrschnabel, Dominik
  %A Stumme, Gerd
  %B Conceptual Knowledge Structures
  %C Cham
  %D 2025
  %E Cellier, Peggy
  %E Ganter, Bernhard
  %E Missaoui, Rokia
  %I Springer Nature Switzerland
  %P 392--407
  %T Rises for Measuring Local Distributivity in Lattices
  %X Distributivity is a well-established and extensively studied notion in lattice theory. In the context of data analysis, particularly within Formal Concept Analysis (FCA), lattices are often observed to exhibit a high degree of distributivity. However, no standardized measure exists to quantify this property. In this paper, we introduce the notion of rises in (concept) lattices as a means to assess distributivity. Rises capture how the number of attributes or objects in covering concepts change within the concept lattice. We show that a lattice is distributive if and only if no non-unit rises occur. Furthermore, we relate rises to the classical notion of meet- and join distributivity. We observe that concept lattices from real-world data are to a high degree join-distributive, but much less meet-distributive. We additionally study how join-distributivity manifests on the level of ordered sets.
  %@ 978-3-032-03364-2
  

• 1.

  Abdulla, M., Hille, T., Dürrschnabel, D., Stumme, G.: Rises for Measuring Local Distributivity in Lattices. In: Cellier, P., Ganter, B., and Missaoui, R. (eds.) SpringerLink. pp. 392–407. Springer, Cham, Switzerland (2025). https://doi.org/10.1007/978-3-032-03364-2_25.

  URLBibTeXEndNoteDOI

  @incollection{Abdulla2025Sep,
  address = {Cham, Switzerland},
  author = {Abdulla, Mohammad and Hille, Tobias and Dürrschnabel, Dominik and Stumme, Gerd},
  booktitle = {Conceptual Knowledge Structures},
  editor = {Cellier, Peggy and Ganter, Bernhard and Missaoui, Rokia},
  journal = {SpringerLink},
  keywords = {itegpub},
  month = {09},
  pages = {392--407},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Rises for Measuring Local Distributivity in Lattices},
  type = {Publication},
  volume = 15941,
  year = 2025
  }
  

  %0 Book Section
  %1 Abdulla2025Sep
  %A Abdulla, Mohammad
  %A Hille, Tobias
  %A Dürrschnabel, Dominik
  %A Stumme, Gerd
  %B Conceptual Knowledge Structures
  %C Cham, Switzerland
  %D 2025
  %E Cellier, Peggy
  %E Ganter, Bernhard
  %E Missaoui, Rokia
  %I Springer
  %J SpringerLink
  %P 392--407
  %R 10.1007/978-3-032-03364-2_25
  %T Rises for Measuring Local Distributivity in Lattices
  %U https://dblp.uni-trier.de/rec/conf/concepts/AbdullaHDS25.html
  %V 15941
  %@ 978-3-032-03364-2
  

• 1.

  Hille, T., Hanika, T.: Incomplete Formal Contexts and Their Intrinsic Dimension. In: Cellier, P., Ganter, B., and Missaoui, R. (eds.) SpringerLink. pp. 342–358. Springer, Cham, Switzerland (2025). https://doi.org/10.1007/978-3-032-03364-2_22.

  URLBibTeXEndNoteDOI

  @incollection{Hille2025Sep,
  address = {Cham, Switzerland},
  author = {Hille, Tobias and Hanika, Tom},
  booktitle = {Conceptual Knowledge Structures},
  editor = {Cellier, Peggy and Ganter, Bernhard and Missaoui, Rokia},
  journal = {SpringerLink},
  keywords = {itegpub},
  month = {09},
  pages = {342--358},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Incomplete Formal Contexts and Their Intrinsic Dimension},
  type = {Publication},
  volume = 15941,
  year = 2025
  }
  

  %0 Book Section
  %1 Hille2025Sep
  %A Hille, Tobias
  %A Hanika, Tom
  %B Conceptual Knowledge Structures
  %C Cham, Switzerland
  %D 2025
  %E Cellier, Peggy
  %E Ganter, Bernhard
  %E Missaoui, Rokia
  %I Springer
  %J SpringerLink
  %P 342--358
  %R 10.1007/978-3-032-03364-2_22
  %T Incomplete Formal Contexts and Their Intrinsic Dimension
  %U https://dblp.uni-trier.de/rec/conf/concepts/HilleH25.html
  %V 15941
  %@ 978-3-032-03364-2
  

• 1.

  Draude, C., Engert, S., Hess, T., Hirth, J., Horn, V., Kropf, J., Lamla, J., Stumme, G., Uhlmann, M., Zwingmann, N.: Verrechnung – Design – Kultivierung: Instrumentenkasten für die Gestaltung fairer Geschäftsmodelle durch Ko-Valuation, https://plattform-privatheit.de/p-prv-wAssets/Assets/Veroeffentlichungen_WhitePaper_PolicyPaper/whitepaper/WP_2024_FAIRDIENSTE_1.0.pdf, (2024). https://doi.org/10.24406/publica-2497.

  URLBibTeXEndNoteDOI

  @misc{claude2024verrechnung,
  address = {Karlsruhe},
  author = {Draude, Claude and Engert, Simon and Hess, Thomas and Hirth, Johannes and Horn, Viktoria and Kropf, Jonathan and Lamla, Jörn and Stumme, Gerd and Uhlmann, Markus and Zwingmann, Nina},
  edition = 1,
  editor = {Friedewald, Michael and Roßnagel, Alexander and Geminn, Christian and Karaboga, Murat},
  howpublished = {White Paper},
  keywords = {itegpub},
  month = {03},
  publisher = {Fraunhofer-Institut für System- und Innovationsforschung ISI},
  series = {Plattform Privatheit},
  title = {Verrechnung – Design – Kultivierung: Instrumentenkasten für die Gestaltung fairer Geschäftsmodelle durch Ko-Valuation},
  year = 2024
  }
  

  %0 Generic
  %1 claude2024verrechnung
  %A Draude, Claude
  %A Engert, Simon
  %A Hess, Thomas
  %A Hirth, Johannes
  %A Horn, Viktoria
  %A Kropf, Jonathan
  %A Lamla, Jörn
  %A Stumme, Gerd
  %A Uhlmann, Markus
  %A Zwingmann, Nina
  %B Plattform Privatheit
  %C Karlsruhe
  %D 2024
  %E Friedewald, Michael
  %E Roßnagel, Alexander
  %E Geminn, Christian
  %E Karaboga, Murat
  %I Fraunhofer-Institut für System- und Innovationsforschung ISI
  %R 10.24406/publica-2497
  %T Verrechnung – Design – Kultivierung: Instrumentenkasten für die Gestaltung fairer Geschäftsmodelle durch Ko-Valuation
  %U https://plattform-privatheit.de/p-prv-wAssets/Assets/Veroeffentlichungen_WhitePaper_PolicyPaper/whitepaper/WP_2024_FAIRDIENSTE_1.0.pdf
  %7 1
  

• 1.

  Draude, C., D{ü}rrschnabel, D., Hirth, J., Horn, V., Kropf, J., Lamla, J., Stumme, G., Uhlmann, M.: Conceptual Mapping of Controversies. In: Cabrera, I.P., Ferr{é}, S., and Obiedkov, S. (eds.) Conceptual Knowledge Structures. pp. 201–216. Springer Nature Switzerland, Cham (2024).

  BibTeXEndNote

  With our work, we contribute towards a qualitative analysis of the discourse on controversies in online news media. For this, we employ Formal Concept Analysis and the economics of conventions to derive conceptual controversy maps. In our experiments, we analyze two maps from different news journals with methods from ordinal data science. We show how these methods can be used to assess the diversity, complexity and potential bias of controversies. In addition to that, we discuss how the diagrams of concept lattices can be used to navigate between news articles.

  @inproceedings{10.1007/978-3-031-67868-4_14,
  abstract = {With our work, we contribute towards a qualitative analysis of the discourse on controversies in online news media. For this, we employ Formal Concept Analysis and the economics of conventions to derive conceptual controversy maps. In our experiments, we analyze two maps from different news journals with methods from ordinal data science. We show how these methods can be used to assess the diversity, complexity and potential bias of controversies. In addition to that, we discuss how the diagrams of concept lattices can be used to navigate between news articles.},
  address = {Cham},
  author = {Draude, Claude and D{ü}rrschnabel, Dominik and Hirth, Johannes and Horn, Viktoria and Kropf, Jonathan and Lamla, J{ö}rn and Stumme, Gerd and Uhlmann, Markus},
  booktitle = {Conceptual Knowledge Structures},
  editor = {Cabrera, Inma P. and Ferr{é}, S{é}bastien and Obiedkov, Sergei},
  keywords = {formal_concept_analysis},
  pages = {201--216},
  publisher = {Springer Nature Switzerland},
  title = {Conceptual Mapping of Controversies},
  year = 2024
  }
  

  %0 Conference Paper
  %1 10.1007/978-3-031-67868-4_14
  %A Draude, Claude
  %A D{ü}rrschnabel, Dominik
  %A Hirth, Johannes
  %A Horn, Viktoria
  %A Kropf, Jonathan
  %A Lamla, J{ö}rn
  %A Stumme, Gerd
  %A Uhlmann, Markus
  %B Conceptual Knowledge Structures
  %C Cham
  %D 2024
  %E Cabrera, Inma P.
  %E Ferr{é}, S{é}bastien
  %E Obiedkov, Sergei
  %I Springer Nature Switzerland
  %P 201--216
  %T Conceptual Mapping of Controversies
  %X With our work, we contribute towards a qualitative analysis of the discourse on controversies in online news media. For this, we employ Formal Concept Analysis and the economics of conventions to derive conceptual controversy maps. In our experiments, we analyze two maps from different news journals with methods from ordinal data science. We show how these methods can be used to assess the diversity, complexity and potential bias of controversies. In addition to that, we discuss how the diagrams of concept lattices can be used to navigate between news articles.
  %@ 978-3-031-67868-4
  

• 1.

  Hirth, J., Horn, V., Stumme, G., Hanika, T.: Ordinal motifs in lattices. Information Sciences. 659, 120009 (2024). https://doi.org/https://doi.org/10.1016/j.ins.2023.120009.

  URLBibTeXEndNoteDOI

  @article{HIRTH2024120009,
  author = {Hirth, Johannes and Horn, Viktoria and Stumme, Gerd and Hanika, Tom},
  journal = {Information Sciences},
  keywords = {itegpub},
  pages = 120009,
  title = {Ordinal motifs in lattices},
  volume = 659,
  year = 2024
  }
  

  %0 Journal Article
  %1 HIRTH2024120009
  %A Hirth, Johannes
  %A Horn, Viktoria
  %A Stumme, Gerd
  %A Hanika, Tom
  %D 2024
  %J Information Sciences
  %P 120009
  %R https://doi.org/10.1016/j.ins.2023.120009
  %T Ordinal motifs in lattices
  %U https://www.sciencedirect.com/science/article/pii/S0020025523015943
  %V 659
  

• 1.

  Draude, C., Dürrschnabel, D., Hirth, J., Horn, V., Kropf, J., Lamla, J., Stumme, G., Uhlmann, M.: Conceptual Mapping of Controversies. In: Cabrera, I.P., Ferré, S., and Obiedkov, S. (eds.) Conceptual Knowledge Structures. pp. 201–216. Springer Nature Switzerland, Cham (2024).

  BibTeXEndNote

  With our work, we contribute towards a qualitative analysis of the discourse on controversies in online news media. For this, we employ Formal Concept Analysis and the economics of conventions to derive conceptual controversy maps. In our experiments, we analyze two maps from different news journals with methods from ordinal data science. We show how these methods can be used to assess the diversity, complexity and potential bias of controversies. In addition to that, we discuss how the diagrams of concept lattices can be used to navigate between news articles.

  @inproceedings{10.1007/978-3-031-67868-4_14,
  abstract = {With our work, we contribute towards a qualitative analysis of the discourse on controversies in online news media. For this, we employ Formal Concept Analysis and the economics of conventions to derive conceptual controversy maps. In our experiments, we analyze two maps from different news journals with methods from ordinal data science. We show how these methods can be used to assess the diversity, complexity and potential bias of controversies. In addition to that, we discuss how the diagrams of concept lattices can be used to navigate between news articles.},
  address = {Cham},
  author = {Draude, Claude and Dürrschnabel, Dominik and Hirth, Johannes and Horn, Viktoria and Kropf, Jonathan and Lamla, J{ö}rn and Stumme, Gerd and Uhlmann, Markus},
  booktitle = {Conceptual Knowledge Structures},
  editor = {Cabrera, Inma P. and Ferré, Sébastien and Obiedkov, Sergei},
  keywords = {itegpub},
  pages = {201--216},
  publisher = {Springer Nature Switzerland},
  title = {Conceptual Mapping of Controversies},
  year = 2024
  }
  

  %0 Conference Paper
  %1 10.1007/978-3-031-67868-4_14
  %A Draude, Claude
  %A Dürrschnabel, Dominik
  %A Hirth, Johannes
  %A Horn, Viktoria
  %A Kropf, Jonathan
  %A Lamla, J{ö}rn
  %A Stumme, Gerd
  %A Uhlmann, Markus
  %B Conceptual Knowledge Structures
  %C Cham
  %D 2024
  %E Cabrera, Inma P.
  %E Ferré, Sébastien
  %E Obiedkov, Sergei
  %I Springer Nature Switzerland
  %P 201--216
  %T Conceptual Mapping of Controversies
  %X With our work, we contribute towards a qualitative analysis of the discourse on controversies in online news media. For this, we employ Formal Concept Analysis and the economics of conventions to derive conceptual controversy maps. In our experiments, we analyze two maps from different news journals with methods from ordinal data science. We show how these methods can be used to assess the diversity, complexity and potential bias of controversies. In addition to that, we discuss how the diagrams of concept lattices can be used to navigate between news articles.
  %@ 978-3-031-67868-4
  

• 1.

  Abdulla, M., Hirth, J., Stumme, G.: The Birkhoff Completion of Finite Lattices. In: Cabrera, I.P., Ferré, S., and Obiedkov, S. (eds.) Conceptual Knowledge Structures. pp. 20–35. Springer Nature Switzerland, Cham (2024).

  BibTeXEndNote

  We introduce the Birkhoff completion as the smallest distributive lattice in which a given finite lattice can be embedded as semi-lattice. We discuss its relationship to implicational theories, in particular to R. Wille's simply-implicational theories. By an example, we show how the Birkhoff completion can be used as a tool for ordinal data science.

  @inproceedings{10.1007/978-3-031-67868-4_2,
  abstract = {We introduce the Birkhoff completion as the smallest distributive lattice in which a given finite lattice can be embedded as semi-lattice. We discuss its relationship to implicational theories, in particular to R. Wille's simply-implicational theories. By an example, we show how the Birkhoff completion can be used as a tool for ordinal data science.},
  address = {Cham},
  author = {Abdulla, Mohammad and Hirth, Johannes and Stumme, Gerd},
  booktitle = {Conceptual Knowledge Structures},
  editor = {Cabrera, Inma P. and Ferré, Sébastien and Obiedkov, Sergei},
  keywords = {itegpub},
  pages = {20--35},
  publisher = {Springer Nature Switzerland},
  title = {The Birkhoff Completion of Finite Lattices},
  year = 2024
  }
  

  %0 Conference Paper
  %1 10.1007/978-3-031-67868-4_2
  %A Abdulla, Mohammad
  %A Hirth, Johannes
  %A Stumme, Gerd
  %B Conceptual Knowledge Structures
  %C Cham
  %D 2024
  %E Cabrera, Inma P.
  %E Ferré, Sébastien
  %E Obiedkov, Sergei
  %I Springer Nature Switzerland
  %P 20--35
  %T The Birkhoff Completion of Finite Lattices
  %X We introduce the Birkhoff completion as the smallest distributive lattice in which a given finite lattice can be embedded as semi-lattice. We discuss its relationship to implicational theories, in particular to R. Wille's simply-implicational theories. By an example, we show how the Birkhoff completion can be used as a tool for ordinal data science.
  %@ 978-3-031-67868-4
  

• 1.

  Hille, T., Stubbemann, M., Hanika, T.: Reproducibility and Geometric Intrinsic Dimensionality: An Investigation on Graph Neural Network Research, (2024).

  BibTeXEndNote

  @preprint{hille2024reproducibility,
  author = {Hille, Tobias and Stubbemann, Maximilian and Hanika, Tom},
  keywords = {intrinsic},
  title = {Reproducibility and Geometric Intrinsic Dimensionality: An Investigation on Graph Neural Network Research},
  year = 2024
  }
  

  %0 Generic
  %1 hille2024reproducibility
  %A Hille, Tobias
  %A Stubbemann, Maximilian
  %A Hanika, Tom
  %D 2024
  %T Reproducibility and Geometric Intrinsic Dimensionality: An Investigation on Graph Neural Network Research
  

• 1.

  Hanika, T., Jäschke, R.: A Repository for Formal Contexts. In: Proceedings of the 1st International Joint Conference on Conceptual Knowledge Structures (2024).

  URLBibTeXEndNote

  Data is always at the center of the theoretical development and investigation of the applicability of formal concept analysis. It is therefore not surprising that a large number of data sets are repeatedly used in scholarly articles and software tools, acting as de facto standard data sets. However, the distribution of the data sets poses a problem for the sustainable development of the research field. There is a lack of a central location that provides and describes FCA data sets and links them to already known analysis results. This article analyses the current state of the dissemination of FCA data sets, presents the requirements for a central FCA repository, and highlights the challenges for this.

  @inproceedings{hanika2024repository,
  abstract = {Data is always at the center of the theoretical development and investigation of the applicability of formal concept analysis. It is therefore not surprising that a large number of data sets are repeatedly used in scholarly articles and software tools, acting as de facto standard data sets. However, the distribution of the data sets poses a problem for the sustainable development of the research field. There is a lack of a central location that provides and describes FCA data sets and links them to already known analysis results. This article analyses the current state of the dissemination of FCA data sets, presents the requirements for a central FCA repository, and highlights the challenges for this.},
  author = {Hanika, Tom and Jäschke, Robert},
  booktitle = {Proceedings of the 1st International Joint Conference on Conceptual Knowledge Structures},
  keywords = {repository},
  title = {A Repository for Formal Contexts},
  year = 2024
  }
  

  %0 Conference Paper
  %1 hanika2024repository
  %A Hanika, Tom
  %A Jäschke, Robert
  %B Proceedings of the 1st International Joint Conference on Conceptual Knowledge Structures
  %D 2024
  %T A Repository for Formal Contexts
  %U https://arxiv.org/abs/2404.04344
  %X Data is always at the center of the theoretical development and investigation of the applicability of formal concept analysis. It is therefore not surprising that a large number of data sets are repeatedly used in scholarly articles and software tools, acting as de facto standard data sets. However, the distribution of the data sets poses a problem for the sustainable development of the research field. There is a lack of a central location that provides and describes FCA data sets and links them to already known analysis results. This article analyses the current state of the dissemination of FCA data sets, presents the requirements for a central FCA repository, and highlights the challenges for this.
  

• 1.

  Horn, V., Hirth, J., Holfeld, J., Behmenburg, J.H., Draude, C., Stumme, G.: Disclosing Diverse Perspectives of News Articles for Navigating between Online Journalism Content. In: Nordic Conference on Human-Computer Interaction. Association for Computing Machinery, Uppsala, Sweden (2024). https://doi.org/10.1145/3679318.3685414.

  URLBibTeXEndNoteDOI

  Today, exposure to journalistic online content is predominantly controlled by news recommender systems, which often suggest content that matches user’s interests or is selected according to non-transparent recommendation criteria. To circumvent resulting trade-offs like polarisation or fragmentation whilst ensuring user’s autonomy, we explore how different perspectives within online news can be disclosed instead for guiding navigation. To do so, we developed an interactive prototype that displays article titles in correspondence to their argumentative orientation. In order to investigate how the usage of our novel navigation structure impacts the choice of news articles and user experience, we conducted an exploratory user study assessing the impact of the design parameters chosen. Implications are drawn from the study results and the development of the interactive prototype for the exposure to diversity in the context of navigating news content online.

  @inproceedings{hci-lattice,
  abstract = {Today, exposure to journalistic online content is predominantly controlled by news recommender systems, which often suggest content that matches user’s interests or is selected according to non-transparent recommendation criteria. To circumvent resulting trade-offs like polarisation or fragmentation whilst ensuring user’s autonomy, we explore how different perspectives within online news can be disclosed instead for guiding navigation. To do so, we developed an interactive prototype that displays article titles in correspondence to their argumentative orientation. In order to investigate how the usage of our novel navigation structure impacts the choice of news articles and user experience, we conducted an exploratory user study assessing the impact of the design parameters chosen. Implications are drawn from the study results and the development of the interactive prototype for the exposure to diversity in the context of navigating news content online.},
  address = {New York, NY, USA},
  author = {Horn, Viktoria and Hirth, Johannes and Holfeld, Julian and Behmenburg, Jens Hendrik and Draude, Claude and Stumme, Gerd},
  booktitle = {Nordic Conference on Human-Computer Interaction},
  keywords = {itegpub},
  publisher = {Association for Computing Machinery},
  series = {NordiCHI 2024},
  title = {Disclosing Diverse Perspectives of News Articles for Navigating between Online Journalism Content},
  year = 2024
  }
  

  %0 Conference Paper
  %1 hci-lattice
  %A Horn, Viktoria
  %A Hirth, Johannes
  %A Holfeld, Julian
  %A Behmenburg, Jens Hendrik
  %A Draude, Claude
  %A Stumme, Gerd
  %B Nordic Conference on Human-Computer Interaction
  %C New York, NY, USA
  %D 2024
  %I Association for Computing Machinery
  %R 10.1145/3679318.3685414
  %T Disclosing Diverse Perspectives of News Articles for Navigating between Online Journalism Content
  %U https://doi.org/10.1145/3679318.3685414
  %X Today, exposure to journalistic online content is predominantly controlled by news recommender systems, which often suggest content that matches user’s interests or is selected according to non-transparent recommendation criteria. To circumvent resulting trade-offs like polarisation or fragmentation whilst ensuring user’s autonomy, we explore how different perspectives within online news can be disclosed instead for guiding navigation. To do so, we developed an interactive prototype that displays article titles in correspondence to their argumentative orientation. In order to investigate how the usage of our novel navigation structure impacts the choice of news articles and user experience, we conducted an exploratory user study assessing the impact of the design parameters chosen. Implications are drawn from the study results and the development of the interactive prototype for the exposure to diversity in the context of navigating news content online.
  %@ 9798400709661
  

• 1.

  Hirth, J.: Conceptual Data Scaling in Machine Learning, (2024). https://doi.org/10.17170/kobra-2024100910940.

  BibTeXEndNoteDOI

  Information that is intended for human interpretation is frequently represented in a structured manner. This allows for a navigation between individual pieces to find, connect or combine information to gain new insights. Within a structure, we derive knowledge from inference of hierarchical or logical relations between data objects. For unstructured data there are numerous methods to define a data schema based on user interpretations. Afterward, data objects can be aggregated to derive (hierarchical) structures based on common properties. There are four main challenges with respect to the explainability of the derived structures. First, formal procedures are needed to infer knowledge about the data set, or parts of it, from hierarchical structures. Second, what does knowledge inferred from a structure imply for the data set it was derived from? Third, structures may be incomprehensibly large for human interpretation. Methods are needed to reduce structures to smaller representations in a consistent, comprehensible manner that provides control over possibly introduced error. Forth, the original data set does not need to have interpretable features and thus only allow for the inference of structural properties. In order to extract information based on real world properties, we need methods that are able to add such properties. With the presented work, we address these challenges using and extending the rich tool-set of Formal Concept Analysis. Here, data objects are aggregated to closed sets called formal concepts based on (unary) symbolic attributes that they have in common. The process of deriving symbolic attributes is called conceptual scaling and depends on the interpretation of the data by the analyst. The resulting hierarchical structure of concepts is called concept lattice. To infer knowledge from the concept lattice structures we introduce new methods based on sub-structures that are of standardized shape, called ordinal motifs. This novel method allows us to explain the structure of a concept lattice based on geometric aspects. Throughout our work, we focus on data representations from multiple state-of-the-art machine learning algorithms. In all cases, we elaborate extensively on how to interpret these models through derived concept lattices and develop scaling procedures specific to each algorithm. Some of the considered models are black-box models whose internal data representations are numeric with no clear real world semantics. For these, we present a method to link background knowledge to the concept lattice structure. To reduce the complexity of concept lattices we provide a new theoretical framework that allows us to generate (small) views on a concept lattice. These enable more selective and comprehensibly sized explanations for data parts that are of interest. In addition to that, we introduce methods to combine and subtract views from each other, and to identify missing or incorrect parts.

  @phdthesis{doi:10.17170/kobra-2024100910940,
  abstract = {Information that is intended for human interpretation is frequently represented in a structured manner. This allows for a navigation between individual pieces to find, connect or combine information to gain new insights. Within a structure, we derive knowledge from inference of hierarchical or logical relations between data objects. For unstructured data there are numerous methods to define a data schema based on user interpretations. Afterward, data objects can be aggregated to derive (hierarchical) structures based on common properties. There are four main challenges with respect to the explainability of the derived structures. First, formal procedures are needed to infer knowledge about the data set, or parts of it, from hierarchical structures. Second, what does knowledge inferred from a structure imply for the data set it was derived from? Third, structures may be incomprehensibly large for human interpretation. Methods are needed to reduce structures to smaller representations in a consistent, comprehensible manner that provides control over possibly introduced error. Forth, the original data set does not need to have interpretable features and thus only allow for the inference of structural properties. In order to extract information based on real world properties, we need methods that are able to add such properties. With the presented work, we address these challenges using and extending the rich tool-set of Formal Concept Analysis. Here, data objects are aggregated to closed sets called formal concepts based on (unary) symbolic attributes that they have in common. The process of deriving symbolic attributes is called conceptual scaling and depends on the interpretation of the data by the analyst. The resulting hierarchical structure of concepts is called concept lattice. To infer knowledge from the concept lattice structures we introduce new methods based on sub-structures that are of standardized shape, called ordinal motifs. This novel method allows us to explain the structure of a concept lattice based on geometric aspects. Throughout our work, we focus on data representations from multiple state-of-the-art machine learning algorithms. In all cases, we elaborate extensively on how to interpret these models through derived concept lattices and develop scaling procedures specific to each algorithm. Some of the considered models are black-box models whose internal data representations are numeric with no clear real world semantics. For these, we present a method to link background knowledge to the concept lattice structure. To reduce the complexity of concept lattices we provide a new theoretical framework that allows us to generate (small) views on a concept lattice. These enable more selective and comprehensibly sized explanations for data parts that are of interest. In addition to that, we introduce methods to combine and subtract views from each other, and to identify missing or incorrect parts.},
  author = {Hirth, Johannes},
  keywords = {Knowldege~Representation},
  school = {Kassel, Universität Kassel, Fachbereich Elektrotechnik/Informatik},
  title = {Conceptual Data Scaling in Machine Learning},
  year = 2024
  }
  

  %0 Thesis
  %1 doi:10.17170/kobra-2024100910940
  %A Hirth, Johannes
  %D 2024
  %R 10.17170/kobra-2024100910940
  %T Conceptual Data Scaling in Machine Learning
  %X Information that is intended for human interpretation is frequently represented in a structured manner. This allows for a navigation between individual pieces to find, connect or combine information to gain new insights. Within a structure, we derive knowledge from inference of hierarchical or logical relations between data objects. For unstructured data there are numerous methods to define a data schema based on user interpretations. Afterward, data objects can be aggregated to derive (hierarchical) structures based on common properties. There are four main challenges with respect to the explainability of the derived structures. First, formal procedures are needed to infer knowledge about the data set, or parts of it, from hierarchical structures. Second, what does knowledge inferred from a structure imply for the data set it was derived from? Third, structures may be incomprehensibly large for human interpretation. Methods are needed to reduce structures to smaller representations in a consistent, comprehensible manner that provides control over possibly introduced error. Forth, the original data set does not need to have interpretable features and thus only allow for the inference of structural properties. In order to extract information based on real world properties, we need methods that are able to add such properties. With the presented work, we address these challenges using and extending the rich tool-set of Formal Concept Analysis. Here, data objects are aggregated to closed sets called formal concepts based on (unary) symbolic attributes that they have in common. The process of deriving symbolic attributes is called conceptual scaling and depends on the interpretation of the data by the analyst. The resulting hierarchical structure of concepts is called concept lattice. To infer knowledge from the concept lattice structures we introduce new methods based on sub-structures that are of standardized shape, called ordinal motifs. This novel method allows us to explain the structure of a concept lattice based on geometric aspects. Throughout our work, we focus on data representations from multiple state-of-the-art machine learning algorithms. In all cases, we elaborate extensively on how to interpret these models through derived concept lattices and develop scaling procedures specific to each algorithm. Some of the considered models are black-box models whose internal data representations are numeric with no clear real world semantics. For these, we present a method to link background knowledge to the concept lattice structure. To reduce the complexity of concept lattices we provide a new theoretical framework that allows us to generate (small) views on a concept lattice. These enable more selective and comprehensibly sized explanations for data parts that are of interest. In addition to that, we introduce methods to combine and subtract views from each other, and to identify missing or incorrect parts.
  

• 1.

  Hirth, J., Hanika, T.: The Geometric Structure of Topic Models, (2024). https://doi.org/10.48550/arxiv.2403.03607.

  BibTeXEndNoteDOI

  @misc{hirth2024geometric,
  author = {Hirth, Johannes and Hanika, Tom},
  keywords = {selected},
  publisher = {arXiv},
  title = {The Geometric Structure of Topic Models},
  year = 2024
  }
  

  %0 Generic
  %1 hirth2024geometric
  %A Hirth, Johannes
  %A Hanika, Tom
  %D 2024
  %I arXiv
  %R 10.48550/arxiv.2403.03607
  %T The Geometric Structure of Topic Models